Geometry of Lie integrability by quadratures

  title={Geometry of Lie integrability by quadratures},
  author={J. F. Cari{\~n}ena and Fernando Falceto and Jacek Grabowski and Manuel Fernandez Ra{\~n}ada},
  • J. F. Cariñena, Fernando Falceto, +1 author Manuel Fernandez Rañada
  • Published 2015
  • Mathematics, Physics
  • In this paper, we extend the Lie theory of integration by quadratures of systems of ordinary differential equations in two different ways. First, we consider a finite-dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way. It turns out that the conditions can be expressed in a purely algebraic way. In the second step, we generalize the construction to the case in… CONTINUE READING

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